Feature-level and decision-level fusion of noncoincidently …people.ee.duke.edu/~lcarin/DeminingMURI/OSU_TPAMI01... · 2002. 3. 27. · methods of fusion. In this paper, we discuss

Feature-Level and Decision-LevelFusion of Noncoincidently SampledSensors for Land Mine Detection

Ajith H. Gunatilaka, Member, IEEE, and Brian A. Baertlein, Member, IEEE

AbstractÐWe present and compare methods for feature-level (predetection) and decision-level (postdetection) fusion of multisensor

data. This study emphasizes fusion techniques that are suitable for noncommensurate data sampled at noncoincident points.

Decision-level fusion is most convenient for such data, but it is suboptimal in principle, since targets not detected by all sensors will not

obtain the full benefits of fusion. A novel algorithm for feature-level fusion of noncommensurate, noncoincidently sampled data is

described, in which a model is fitted to the sensor data and the model parameters are used as features. Formulations for both feature-

level and decision-level fusion are described, along with some practical simplifications. A closed-form expression is available for

feature-level fusion of normally distributed data and this expression is used with simulated data to study requirements for sample

position accuracy in multisensor data. The performance of feature-level and decision-level fusion algorithms are compared for

experimental data acquired by a metal detector, a ground-penetrating radar, and an infrared camera at a challenging test site

containing surrogate mines. It is found that fusion of binary decisions does not perform significantly better than the best available

sensor. The performance of feature-level fusion is significantly better than the individual sensors, as is decision-level fusion when

detection confidence information is also available (ªsoft-decisionº fusion).

Index TermsÐLand mines, sensor fusion, infrared, ground penetrating radar, metal detectors.

æ

1 INTRODUCTION

BURIED land mines are an extremely hazardous fact of lifefor civilians in many countries. Various estimates put

the number of buried landmines worldwide at over80 million and growing. The extreme risk posed by minesimplies that a mine sensor should have essentially nomissed detections. This requirement and the clutter-richenvironment in which mine sensors operate leads to highfalse alarm rates. Nonetheless, low false alarm rates arerequired because of the large land areas where mineclearance is necessary and the cost of clearing a putativemine. Several sensor technologies have been considered forthe detection of mines, including electromagnetic induction(EMI), ground penetrating radar (GPR), infra-red (IR)imaging, quadrupole resonance (QR), various chemicaldetectors (e.g., electronic ªsniffersº), and sensors of acous-tically induced surface vibrations. At present, none of thesetechnologies has proven to be acceptably effective andreliable for the wide range of mines and environmentalconditions encountered in the field.

Because of the diverse physical properties measured

by different sensor technologies, multisensor fusion is

attractive as a means of improving mine detection.

Unfortunately, demining sensor fusion is hindered byseveral factors. First, sensors used for mine detectiontypically produce noncommensurate data, i.e., data thatare not of comparable form and, hence, are not easilycombined. By way of example, three commmonly usedmine sensors are IR cameras, which produce surfaceimagery; ground penetrating radars which produce depthprofiles along a line scan; and metal detectors, whichproduce scalar measurements along a line scan. Evenwhen the data are commensurate, the sensors mayoperate on different platforms, leading to noncoincidentsampling and problems with data registration. Sincefusion comprises combining information from multiplesources regarding a specified phenomenon (e.g., thepresence of a mine) at a specific location, accomodatingnoncoincident samples is a necessity.

Some of these concerns can be alleviated by decision-level fusion, in which the operator performs detection at thesensor level and then combines (fuses) detections fromindividual sensors. This process reduces diverse sensor datato a common format (binary decisions or detection prob-abilities), which are readily combined using conventionalstatistical techniques. A variety of techniques have beendeveloped for this approach [1], [2].

In principle, however, decision-level fusion is subopti-mal since if a target is not detected by all sensors, it will notexperience the full benefits of fusion. This situation andstressing performance requirements, led us to explore othermethods of fusion. In this paper, we discuss a feature-levelfusion approach to noncoincident sensor sampling. Thedata are represented by a model with unknown parameters(features) and random additive clutter. Optimization

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 23, NO. 6, JUNE 2001 577

. A.H. Gunatilaka is with Lucent Technologies, 6200 E. Broad Street,Columbus, OH 43213.

. B.A. Baertlein is with The Ohio State University, ElectroScienceLaboratory, 1320 Kinnear Road, Columbus, OH 43212.E-mail: [email protected].

Manuscript received 8 Feb. 2000; revised 28 Nov. 2000; accepted 14 Dec.2000.Recommended for acceptance by R. Beveridge.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number 111425.

0162-8828/01/$10.00 ß 2001 IEEE

techniques are used to determine features from theavailable data, and classification is performed on the basisof the features. The effects of sample position uncertaintyare also examined for the case of normally distributedfeatures.

Fusion of demining sensor data has been investigatedpreviously. Chauduri et al. [3] developed a deminingsystem in which coregistered GPR and EMI sensors werefused using several decision-level fusion approaches. Brus-mark et al. [4] demonstrated the decision-level fusion ofcoincidently sampled GPR and EMI sensor data collectedover targets buried in a sand box. Clark et al. [5] fused twoIR sensors of different wavelengths, which were registeredusing a set of fiducial markers. A neural network-basedfeature-level fusion approach was used in that work.Miao et al. considered the fusion of six coregisteredIR images corresponding to different wavelengths [6]. Eachimage was separately classified with neural networks andthe resulting decisions were fused using both majorityvoting and a consensus theory approach. Weisenseel et al.[7] studied decision-level fusion of GPR and EMI data usingsynthetic data. The problem was greatly simplified byassuming that the mines were detectable by both sensors,metallic clutter by EMI alone and nonmetallic clutter byGPR alone. Only an AND rule was considered for fusion.Breejen et al. [8] compared several methods for decision-level fusion of EMI, GPR, and IR data. They used the samedata for both training and testing the classifiers, which oftenyields optimistic results. The performance of a vehiclemounted mine detector employing GPR, EMI, and videoand IR cameras, developed by EG&G Management Sys-tems, Incorporated, was reported in [9]. While surfaceemplaced antitank mines and mines with significant metalcontent were easily detected, buried plastic mines werefound to be challenging. Development and testing of avehicle-mounted multisensor demining platform that usesEMI, GPR, and IR for detection and a TNA sensor for targetconfirmation is underway at the Canadian Defence Re-search Establishment [10]. Gunatilaka and Baertlein [11]compared predetection (feature-level) and postdetection(hard and soft decision-level) fusion of EMI, GPR, andIR data. A benefit was observed for feature-level fusion, andfusion of soft decisions was found to be better than fusion ofhard decisions. Gunatilaka and Baertlein [12] comparedseveral methods for feature extraction and several fusionstrategies. In all cases, feature-level fusion was found to besuperior to decision-level fusion. Baertlein [13] recentlyinvestigated the problem of constructing fusion algorithmswith limited training data. Using approaches based onStatistical Learning Theory for feature-level fusion and jointoptimization of local decision thresholds for hard decisionfusion, it was shown that algorithm performance could beimproved. For the specific training data used in that work,superior performance was noted for hard decision fusion.Marble et al. [14] demonstrated the benefits of using harddecision-level fusion to combine EMI, GPR, and magnet-ometer data for detection of mines with large metal content.In that work, significant problems with misregistration ofnoncommensurate sensors were overcome by converting all

sensor outputs to a scalar, image-like format and inter-polating the result.

The work reported here complements and extends theprior studies in several respects. First, we consider bothfeature-level and decision-level fusion of experimental datafrom noncommensurate (EMI, GPR, and IR) sensors.Second, we investigate the benefits of fusion under morerealistic conditions by using a test site containing largeamounts of clutter and having an irregular surface. Finally,each sensor was used on a different platform, which led usto consider the effects of noncoincident sampling andpositioning errors.

The work is organized in three major sections. InSection 2 we describe the theoretical basis for feature-levelfusion of noncoincident samples. The basis for decision-level fusion is presented in Section 3. Experimental data andexamples of fusion are given in Section 4. For a list ofsymbols referenced in this paper, see Table 1. Finally,concluding remarks appear in Section 5.

2 FEATURE-LEVEL FUSION OF RANDOMLY

SAMPLED MULTISENSOR DATA

2.1 Problem Definition

Suppose that a suite of NS countermine sensors are usedto acquire data in a region. Sensor i acquires Jidata samples di at locations Rij, which we denotedij � di�Rij�. Fusion is to be performed on the data setD � fdi�Rij�; i � 1; . . . ; Ns; j � 1; . . . ; Jig. We assume thatdifferent sensors produce samples that differ in numberJi, sample positions Rij, format, and the dimensionalityof their data.

Let R be a point where we wish to determine thepresence of a mine. We refer to R as the ªinterrogationpoint.º We form the K hypotheses Hk�R�, k � 1; 2; . . . ; Kfor the fused suite regarding the presence or absence ofvarious types of mines at R. We may also include in the setfHk�R�g discrete clutter objects, e.g., buried rocks, metallicclutter, etc. The explicit dependence of these hypotheses onthe interrogation point is omitted hereafter in the interest ofbrevity.

The decision criterion for the fusion processor is theBayes risk. At each point R, we determine the hypothesisHk that minimizes the riskR conditioned on the data D, viz:

k � arg minjRj�D� � arg min

j

XK`�1

Cj` Pr�H`jD�; �1�

where Rj�D� is the risk of selecting hypothesis Hj givendata D, and Cij is the cost of choosing Hi when Hj is true.If all costs are equal or for the special case K � 2 (binarydetection), it is sufficient to compute the likelihood ratioand to compare it to a threshold. In general, however,multiple hypotheses may be involved and equal costs areinappropriate for the mine-detection problem. It is difficultto assign costs in the mine-detection problem but,fortunately, fusion can be explored without knowledge ofthe costs. Results are reported here in a manner indepen-dent of cost, specifically, a posteriori probabilities Pr�HkjD�and ROC curves are computed. When suitable costs areknown, one can use the general formulation given above to

578 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 23, NO. 6, JUNE 2001

derive the minimum risk decision from the a posterioriprobabilities. Similarly, knowledge of the costs permits oneto readily determine minimum risk operating points on aROC curve.

2.2 Fusion of Noncoincidently Sampled Features

We assume that sensor i acquires at a point Rij data di�Rij�,which lies in the vicinity of a putative target of type k at R.This data is modeled as a signal gi�Rij; �ik� corrupted byadditive clutter (and noise) ni�Rij�, viz:

di�Rij�jHk � gi�Rij; �ik� � ni�Rij�; �2�where �ik is a feature vector (i.e., a set of modelparameters) that describes the signature of targets of typek for sensor i (see Fig. 1). We assume that the clutter ni�R� isindependent of the parameter �ik. Note that, if the clutterdiscretes are also assigned specific hypotheses Hj, thephenomena modeled by ni�R� can be relatively smooth.

For each sensor, the presence of a mine produces ameasurable response over a finite spatial region and, hence,only a subset of D may be relevant to interrogation of theregion around R. Let the relevant data for sensor i be given

by subsequences j1; j2; . . . ; jMiwith length Mi. It is con-

venient to assemble this reduced data set into the vectors

D � d1�R1j1� � � � d1�R1jM1�

hd2�R2j1

� � � � dNs�RNsjMNs

�iT

�3�

N � n1�R1j1� � � � n1�R1jM1�

hn2�R2j1

� � � � nNs�RNsjMNs

�iT �4�

Gk��k� � g1k�R1j1 ; �1k�� gNsk�RNsjMNs

; �Nsk�iT: �5�

If a single datum di�R� from sensor i has length NDi,

then the length of these column vectors is NE �P

i NDiMi.

Using this notation, we have for the combined signal model

DjHk � Gk��k� �N, where the combined (concatenated)

feature vector for all sensors is

�k � �1k �2k � � � �Nsk� �T : �6�

GUNATILAKA AND BAERTLEIN: FEATURE-LEVEL AND DECISION-LEVEL FUSION OF NONCOINCIDENTLY SAMPLED SENSORS FOR LAND... 579

TABLE 1List of Symbols

To support both decision-level fusion and feature-level

fusion with uncertain sample locations, we include in �ik a

position offset R0;ik that describes the nominal ªcenterº of

the mine signature with respect to R and we write

�ik � �ik R0;ik

� �T. In general, we take �ik and R0;ik to be

independent in what follows.

2.3 Approximate Forms

Feature-level fusion of the foregoing data can be formulated

along two lines. Consider first the direct approach using the

a posteriori probabilities, which avoids the problem of

estimating the a priori probabilities. Minimizing the risk in

(1) leads us to consider the a posteriori probabilities as an

integral over the classifier Pr�Hkj�k�

Pr�HkjD� �Zd�k Pr�Hkj�k�f�jD��k�; �7�

in which we have assumed that Hk is determined by �k

alone and, hence, Pr�Hkj�k;D� � Pr�Hkj�k�. This expres-

sion is exact, but it requires knowledge of the density f�jDand that we perform an integral over a feature space of

possibly high dimensions. To avoid these issues, it is

attractive to employ the maximum a posteriori (MAP)

approximation. If the data D strongly imply the value �̂

and the features �k are not too specific (i.e., the maximum

of Pr�Hkj�k� is relatively broad), then f�jD will be strongly

peaked about �̂ and we have

Pr�HkjD� � Pr�Hkj�̂�Zd�kf�kjD��k� � Pr�Hkj�̂�: �8�

Conversely, if D provides no information about �, then

f�jD�� f�� and Pr�HkjD� reduces to the a priori

probability.Feature-level fusion can also be formulated using class-

conditioned densities, and this approach will be used in our

study of sensor position errors. Bayes' rule leads to

Rk�D� � 1

fD

XKj�1

Cjk Pr�Hj�fDjHj�D�: �9�

The a priori probabilities Pr�Hj� are required but, sincethose probabilities are seldom known, this approach issomewhat less attractive in practice. The factor �fD�ÿ1 iscommon to all Rk�D� and, hence, our primary task is toevaluate the class-conditioned probabilities fDjHj

�D�. SinceGk is presumed known, the data D conditioned on theparameter �k has the same density as the clutter N, whichleads to fDj�k;Hk

�D� � fN�DÿGk��k�� and

fDjHk�D� �

Zd�kf�k jHk

��k�fN�DÿGk��k��: �10�

We approximate this exact result as done in (8). Assumingthat fN�DÿG��k�� has a well-defined maximum for �k ��̂k and that f�kjHk

is not strongly peaked leads to

fDjHk�D� � f�kjHk

��̂k�Zd�kfN�DÿGk��k��

� Ekf�kjHk��̂k�fRojHk

�R̂0;k�;�11�

where we have approximated �ik and R0;ik as conditionallyindependent, and the constant factor

Ek �Zd�kfN�DÿGk��k�� 12�

is related to the residual error.

For the two class problem (K � 2), a likelihood ratio

formulation is possible. The likelihood ratio for a known

signal with unknown parameters is given by

��D� � fDjH1�D�

fDjH0�D� �

Rd�f�jH1

��fN�DÿG1��Rd�f�jH0

��fN�DÿG0�� : �13�

If the same model is used for both hypotheses, thenapproximating the results as proposed above yields

��D� � f�jH1��̂1�

Rd�fN�DÿG1��

f�jH0��̂0�

Rd�fN�DÿG0��

� f�jH1��̂1�

f�jH0��̂1�

E1

E0;

�14�where�̂k is theestimateof� thatmaximizesfN�DÿGk��k��under Hk. Detection is performed on the basis of the class-

conditioned densities of �.

It is interesting to compare this formulation to the more

conventional generalized likelihood ratio test (GLRT)

[15, p. 38]. In the GLRT formulation, the model parameters

� are estimated using the maximum likelihood technique.

This leads to the expression

�G�D� �max�1

fDj�1;H1

max�0fDj�0;H0

� fN�DÿG1��̂1��fN�DÿG0��̂0��

: �15�

Thus, GLRT detection is based primarily on the distribution

of the model error. The model parameters are considered

indirectly, via their contribution to the error. The estimator-

correlator method [15, p. 79] uses a similar approach, in which

the parameters are estimated and the resulting model

signature is correlated with the data. For Gaussian statistics,


Fig. 1. The data model for three hypotheses k � 0; 1; 2. For each sensori data di�Rij� are available. For hypothesis k, the sensor data isrepresented by a known function gik�R; �ik�� of position R and randomparameters �ik. The reference position of signature gik is given by R0;ik.The signature parameters �ik, which include the reference position R0;ik

are estimated from the data. In this example, k � 0 corresponds to theno-target case, k � 1 is a target with a unimodal signature, and k � 2 is atarget with a bimodal signature. The objective of fusion is to determine ifa target exists at any point R on the basis of data from multiple sensors.

detection is based on the correlation. The feature-level fusion

algorithm described above could be referred to as an

ªestimator-classifierº technique in that detection (or classifi-

cation) is based on the parameters rather than the residual

error in the model. We will also find it useful to include in the

parameter vector �k, a factor related to the integrated residual

error density Ek, typically, in the form of the error energy.

2.4 Gaussian Approximation

The case of Gaussian statistics is of interest because it

provides insight into the problems of feature-level fusion

and because it can be used to efficiently simulate the

performance of certain fusion strategies. With certain

assumptions, the expression for fDjHkin (10) can be

evaluated in closed form.Consider first, the case in which only the clutter N has a

Gaussian density. That is, the Ns random variables Ni�Rij�(each of which are evaluated at Mi locations) have adensity that is jointly normal with mean �N and covariancematrix CN .

Now, make the additional assumption that the minesignature shape matrix Gk is known (including theunderlying mine positions R0;ik) up to an unknownsignature amplitude. Taking �k to be this amplitude, wemake the linear approximation Gk��k� � ~Gk�k in which~Gk is a known constant vector independent of �k. If thefeatures �k are also Gaussian distributed with density�kjHk � N��k

;C�k�, we obtain the Bayesian linear model

[16, p. 326], which leads to

fD�DjHk� � �2��ÿNE=2eÿQk=2

det�CN�1=2det�C�k�1=2det�Cÿ1

�̂k�Cÿ1

�k�1=2

; �16�

where NE is the length of these vectors (defined previously)and

Qk � Dÿ ~Gk�̂k ÿ �N� �T

Cÿ1N Dÿ ~Gk�̂k ÿ �N� �

�

�̂k ÿ ��k

� �TC�̂ �C�k

ÿ �ÿ1�̂k ÿ ��k

� �:

�17�

In this result, the quantity �̂k is the maximum-likelihoodestimate (MLE) for the feature vector �k, given by

�̂k � C�̂k

~GTkCÿ1

N Dÿ �N� � �18�and Cÿ1

�̂k� ~GT

k Cÿ1N

~Gk is its covariance. The terms of (17), weinterpret as errors due to random clutter and to featurevariability, respectively. Since the first term in (17) isidentical to that arising in fDj�̂;Hk

, it is clear that theGLRT approximation of (15) ignores the second term in (17),which describes the feature distribution.

2.5 Sample Position Errors

We noted earlier that to fuse multisensor data, it isnecessary to know what locations in the environment arerepresented by the data, so that one can make a statementabout the presence of a target the ªinterrogationº point. Inpractice, errors in sample position are largely unavoidable,especially when the sensors are located on different plat-forms. Some common types of sample errors include

uniform offsets produced by a baseline error, linearlyincreasing offsets produced by a drift in position baseline,isotropically distributed errors due to sample-to-samplepositioning inaccuracy, and combinations of the above.

When position errors are present, the sample positionRij has the form R̂ij � rij, where R̂ij is the intendedposition and rij is an unknown error. Thus,

di�Rij�jHk � gk�R̂ij � rij; �� n�R̂ij � rij�:Using a Bayesian approach and making the additionalassumption that the sample positions are independent ofthe mine signature �k and of the hypothesis Hk, theserandom variables are integrated out as follows:

fDjHk�D� �Z

dr1j1

Zdr1j2 � � �

ZdrNsjMNs

fr1j1;r1j2

;...;rNsjMNs

�r1j1 ; r1j2 ; . . . ; rNsjMNs�Z

d�kf�kjHk��k�fN1j1

;...;NNsjMNs

d1j1 ÿ g�R̂1j1 � r1j1; �1k�; . . . ;

�dNsjMNs

ÿ g�R̂NsjMNs� rNsjMNs

; �Nsk�i:

�19�The effect of position errors on system performance for

feature-level fusion was studied using this result and the

Bayesian linear model described in (16). If modest numbers

of sensor data points are being fused at each interrogation

point, the resulting integrals can be numerically evaluated

using Monte Carlo techniques. Gaussian-distributed fea-

tures were simulated for three sensors with isotropically

distributed errors around an intended sample point. The

position errors were normally distributed with variance �2.

The sensor signature models gik were taken to be zero when

the mine was absent and Gaussian functions with variance

�2i when the mine was present. A single feature was

simulated for each sensor and a common value �i � � was

used for all sensors. The ºfeature-to-noiseº ratio��var��ik�=var�Nik�

p(an analog of the signal-to-noise ratio

for this problem) was set to two.It was found that system performance in the presence of

isotropic position errors could be roughly characterized by

the ratio �=�. Figs. 2, 3, and 4 show the results for

�=� � 0:5, 1, and 1.5, respectively. (The case of a random

offset was also examined. The results were similar and are

not shown.) We see that for �=� < 1 the performance of the

classifier is not significantly affected by position offsets, but

for �=� > 1 there is a significant degradation in perfor-

mance. These results suggest the intuitively reasonable

finding that the performance of feature-level fusion systems

will not be adversely effected if the positioning errors are

smaller than the extent of the measurable target signature.

When this condition is violated, fusion becomes less

effective since all sensors may not see the target.It is worth noting that position-related errors can

sometimes be overcome through ingenuity on the part of

the analyst and, hence, these results should be viewed as

suggestive only. For example, when the position errors

comprise constant offsets and the individual sensor

performance is good (i.e., high probability of detection


and low false alarm rates), the offset might be estimated by

registering the detections with those of other sensors. Such

conditions, however, are uncommon in mine detection.

3 DECISION-LEVEL FUSION

The formulation of an optimal decision-level fusion

algorithm is similar to that defined in Section 2 for

feature-level fusion. As before, each sensor i collects data

fdi�Ri1�; . . . ;di�RiMi�g. On the basis of these data, it makes

an intermediate declaration ui regarding the truth

of intermediate sensor-specific hypotheses hiq�R�for q � 1; 2; . . . ; Qi. For example, a sensor suite that

comprises EMI, GPR, and IR sensors might use Qi � 2 for

all i with h11=12 � ªmetallic object present/not present,º

h21=22 � ªdielectric discontinuity present/not present,º and

h31=32 � ªthermal anomaly present/not presentº rather

than simply H1=2 � ªmine present/not present.º In whatfollows, we restrict our attention to the case of equalnumbers of intermediate hypotheses Qi � Q.

3.1 General Formulation

The goal of fusion is to combine these declarations into afused declaration u0 that addresses hypotheses Hk,k � 1; 2; . . . ; K. Each detection ui also involves a thresholdti, which must be specified by the operator. To simplifythe notation, form the vector of individual declarationsgiven by U � u1 u2 . . . uNs

� �T and the threshold vectorT � t1 t2 . . . tNs

� �T . The declarations U and thresholds T

are assumed to be the only data on which the decision u0

is based. In particular, it is assumed that the fusionprocessor has no knowledge of the sensor data D. It isfurther assumed that, for each sensor i, the detectionconfidences Pr�uijhiq� and the a priori probabilities Pr�Hk�are known for all k.

For optimal decision-level fusion, we seek a rule forfusing U into u0 such that the Bayes risk is minimized. Wecan write this risk in the form

R �XU

XKj�1

XKk�1

Cjk Pr�Hk�Pr�u0 � jjU�Pr�UjHk; T�" #

;

�20�which makes explicit the fusion rule Pr�u0 � jjU�. In this

result, the summation on U is over all possible combina-

tions of sensor outcomes and the decision u0 is based only

on the local decisions ui. The individual decisions uiaddress the hypotheses hiq, which are related to Hk in a

manner that implies the following:

Pr�UjHk; T� �XQq�1

Pr�UjHq; T�Pr�HqjHk�; �21�

where Hq � h1q h2q . . . hNsq

� �and we have used the fact

that decision ui depends on hiq and not on Hk. It remains to


Fig. 3. The ROC curve for simulated data with normalized position errors

�=� � 1. Performance degrades as a result of sensor position errors.


�=� � 1:5. Sensor position errors are so large that fusion is ineffective.


�=� � 0:5. Performance is essentially perfect.

specify the fusion rule Pr�u0 � jjU� that will minimize thebracketed quantity in (20). Some approaches are discussedin the following sections.

3.2 An Optimal Hard-Decision Fusion Rule

For sensors that produce ªhardº decisions (i.e., all-or-nothingdeclarations), the fusion rule is a mapping from the Ns-foldproduct of the space f1; 2; . . . ; Qg to one of K outputhypotheses. There exist KQNs

such mappings and, from this(possibly large) set, one must determine the most effectiverule. In general, the most effective mapping will depend onthe effectiveness of the individual sensors. Ad hoc mappings(AND, OR, majority voting, etc.) have been used, some withconsiderable success.

In some situations, there exist optimal mappings fordecision-level fusion [1, xx 3.3, 3.4]. Consider the simplestcase in which the local decision rules (i.e., the mappingsfrom D to the local decisions ui) are fixed and the sensorsoutput hard decisions. For K � Q � 2, the minimum in (20)reduces to a well-known likelihood ratio test, given by

Pr�UjH1; T�Pr�UjH0; T�

u0�1>

<u0�0

�; �22�

where � is the threshold for the fused decision and isindependent of T. If the declarations ui are conditionallyindependent for each sensor,1 then we can factor the jointprobabilites into a product. Defining miss and false alarmprobabilities for each sensor as follows:

PMi�ti� � Pr�ui � 0jH1; ti� �23�PFi�ti� � Pr�ui � 1jH0; ti� �24�

and taking the logarithm of the likelihood-ratio test, we canwrite this optimum test as

XNs

i�1

ui log1ÿ PMi�ti�PFi�ti�

� ��

�

�1ÿ ui� logPMi�ti�

1ÿ PFi�ti�� u0�1

>

<u0�0

�:

�25�

It is easy to see that the logarithms in this expression have alarge magnitude for reliable sensors and, hence, the optimaldecision fusion rule makes fused decisions that aredominated by the reliable decisions.

Since the Bayes risk can also be written in terms of the aposteriori probabilities Pr�HkjU�, we can use anotherapproach to derive the fusion rule. A simple (but notnecessarily optimal) approach is to select u0 such that the aposteriori probability Pr�HkjU� is maximized [17, x 6.3]. Wewrite the a posteriori probability as follows:

Pr�HkjU; T� �YNs

i�1

Pr�uijHk; ti�" #

Pr�Hk�=Pr�U; T�; �26�

where we have invoked the conditional independence of thesensors. This result can be evaluated using known values forPr�uijHl; ti�, which are specified by PFi

�ti� and PMi�ti�.

Note that in both formulations Pr�HkjU� dependsimplicitly on the thresholds T. Optimal fusion requiresthat we select T to produce the best performance. Formodest numbers of sensors, a search over all combinationsof T is possible, but, in general, the search may beimpractical. In such cases, it is more attractive to select avalue of ti that produces ªgoodº sensor performance and touse that threshold for the calculations described above.

3.3 Soft Decision-Level Fusion

Consider the situation in which sensor i reaches decisionui on

the basis of features �i computed from its data using a

deterministic transformation, e.g., Fi�Di� � �i. The hard

decision-level fusion rules in (25) and (26) use global sensor

reliability information in the form of Pr�uijHk; ti� and the

prior probabilities Pr�Hk�, but they do not utilize information

about the confidence each sensor places in its individual

decisions. Such information is quantified by Pr�uij�i; ti�.When the sensors output this local confidence information,

the outputs are equivalent to ªsoftº decisions and we can

perform fusion using an approach similar to that described

above for feature-level fusion. Treating the U as features

returned by each sensor, a discrete analog of (7) yields

Pr�Hkj�� XQu1�1

. . .XQuNs�1

Pr�HkjU�Pr�u1j�1; t1�

Pr�u2j�2; t2� . . . Pr�uNsj�Ns

; tNs�;

�27�

where we have assumed that the fused hypothesis Hk

depends only on the individual sensor decisions ui. Thequantity Pr�HkjU� is computed as described in the harddecision case.

4 EXAMPLE RESULTS: FUSION OF EXPERIMENTAL

DATA

To test the foregoing algorithms, a sensor suite was used toacquire experimental data over a surrogate mine field, andthe resulting data were fused using feature-level anddecision-level techniques. In this section, we describe thesensors, the mine field, and the fused system performance.

4.1 Sensors

The sensor suite used in this work comprised a commercialelectromagnetic induction (EMI) sensor, a ground penetrat-ing radar (GPR), and a commercial infrared (IR) camera.The sensors and the signal processing used in featureextraction are documented below.

4.1.1 Electromagnetic Induction (EMI) Sensor

Virtually all land mines in use today contain some metal,which may be detected by a metal detector. The quantity ofmetal used varies widely from several kilograms to a fewhundred milligrams. Excessive false alarm rates arise whendetecting mines with small metal content because of the largeamount of metallic clutter of anthropic origin found in mostminefields.

The EMI sensor used in this work was a commerciallyavailable pulsed-induction metal detector, the SchiebelAN-19/2 (Schiebel Instruments, Incorporated, Washington,


1. Some physical phenomena (e.g., a small depression in the soil) canhave an effect on several sensors and, hence, this assumption can bedifficult to justify. Nonetheless, it is commonly used in fusion studies.

D.C.) Internal signals within the device were sampled witha digital oscilloscope. The sensor was fitted to a linearscanner, which was used to acquire 56 samples over a55 inch scan. Scans were performed at regularly spacedintervals (nominally every six inches) over the region ofinterest to obtain a grid of sample points.

Signal processing for the EMI sensor is a multistepprocess. The sensor response acquired over soil known tobe metal-free, is subtracted from the waveforms. Theintegral of the resulting difference signal is an effectivedetector of buried metal. The integrated values acquiredalong a scan form spatial signatures. For targets not too nearthe sensor head and not too large compared to the loopradius, the sensor's spatial response has a monopolar shapethat is reasonably well approximated by the function

G1�R; �1� � B� S

1� jRÿR0j=a� �b ; �28�

where R0 is the location of the target's centroid, B is theresponse of the background, S is the amplitude of the targetresponse, and a and b are shape parameters. A moresophisticated physics-based model of the response of aburied sphere has been presented by Das et al. [18] andcould be used as an alternative model, but the simpleempirical form above was adequate to approximate thelimited set of targets considered here.

The second step in EMI signal processing involvesthe estimation of the feature vector �1 given by�1 � �a b S E R0�T . Note that the background level B isnot used in �1 and we have added the quantityE � jDÿGj2=jDj2, which is the residual error in theestimate normalized to the signal energy. To compute�1 at each sample position R, a spatial window wasdefined and the data D1 within this window were fittedto the model using a nonlinear optimization technique.Since stronger signals tend to persist over largerdistances, the size of the window was adjusted on thebasis of the signal amplitude.

4.1.2 Ground Penetrating Radar

A ground penetrating radar detects the presence ofreflecting boundaries in the soil. Such boundaries occur atthe surface of the ground and at most buried objects. A GPRwill detect both metallic and metal-free objects and, hence,it is a useful complement to the metal detector. Unfortu-nately, voids, stones, changes in soil density and moisturecontent, and many other subsurface natural objects are alsodetected, leading to a high false alarm rate.

The GPR used in this effort was developed at The OhioState University (OSU), ElectroScience Laboratory(ESL) [19]. It employs a novel dielectric rod antenna thatwas scanned horizontally over the earth at a fixed height(nominally two inches). A network analyzer was used tomeasure the complex reflection coefficient at 51 frequenciesbetween 1 and 6 GHz. Approximately 100 samples wereacquired on each scan, which had a length of 55 inches. Theantenna and its supporting platform were advanced in twoinch intervals, resulting in a grid of samples.

Calibration of the radar was performed via a two stepprocess. A ªbackgroundº signature (the response of the radarwhen the antenna points into free space) was acquired and

subtracted from all data. The temporal impulse response ofthe radar was then determined by measuring the (back-ground-free) field scattered from a reference target (a shortcylinder) in free space. The ideal scattered field for this targetis known from numerical calculations and the ratio of themeasured and ideal frequency-domain responses yields theimpulse response of the radar. This response is thendeconvolved from the measured data using frequency-domain division. By design, the spectral response of thereference target contains no zeroes, and regularization wasnot found to be necessary in this work.

Processing of the GPR data begins with calibration, inwhich the response of the system is deconvolved from themeasured data. A Fourier transform of the calibrated data isthen used to produce a map of the reflection coefficient as afunction of along-scan position and time (or depth). The datais contaminated by a surface-reflected waveform, which weremove using an OSU-developed technique [11] based on alocal, spatially varying maximum-likelihood estimate of theground position and reflection coefficient. The resulting dataare modeled as a point scatterer plus clutter, the signature ofwhich at a typical depth in homogeneous soil is known anddefines G2�R�. Target depth has an effect on both thesignature shape and time delay, but, because the range ofmine burial depths is restricted, the effect of depth errors ontarget shape was found to be insignificant. The GPR featurevector is given by �2 � � d R0� �T , where � is the peakcorrelation coefficient for the model signature and data, andd and R0 are, respectively, the depth and horizontal positionindicated by the correlation peak. Although false targets areoften seen in GPR scans, they tend not to persist acrossadjacent scans and, hence, the correlation was computed overa three-dimensional (depth, along-scan, and cross-scan) datawindow. GPR data tend to be highly correlated along a scan,because of returns from plane-stratified media and antennaringing not eliminated by calibration. A modest amount ofwhitening was performed prior to correlation.

4.1.3 Infrared Camera

The natural heating and cooling of soil that occurs over adiurnal cycle causes thermal energy to flow into and out ofthe earth. The presence of a buried object changes thisthermal flow, leading to temperature anomalies above theburied object at certain times in the diurnal cycle. Theseanomalies can be detected in soil temperature maps createdby a suitable infrared (IR) camera. Since a mine's thermalproperties are only weakly related to its metal content andelectromagnetic properties, passive IR imaging is presumedto be a good adjunct to EMI and GPR sensors. In addition toburied mines, naturally occuring buried objects (e.g.,stones), variations in soil mineral and water content andvariations in solar illumination (due to shadowing byfoliage, for example) also produce temperature anomalies.Our sensor was a commercially available MWIR camera, theIRRIS 160ST, (Cincinnati Electronics, Cincinnati, OH).

The IR data was processed by first remapping the imageryto ground coordinates using a standard perspective trans-formation [20], followed by bilinear interpolation of thedistorted pixels and resampling to a uniform pixel size. Animage chip was extracted at each interrogation point R.


Based on empirical observations, we employed a signaturemodel identical to that used for the EMI sensor, namely,

G3�R; �� B� S

1� �jRÿR0j=a�b: �29�

The feature vector is �3 � �a b S E R0�T , where E is thenormalized residual error energy.

4.2 Test Site

A surrogate mine field was created to test our sensors underconditions that approximate those found in field situations.The site location, adjacent to our laboratory, is former farmland. A total of 40 mine-like and clutter-like targets wereemplaced in a 4� 10 grid, as shown in Fig. 5. Anabbreviation identifying the buried object and the depthin inches is shown near each object in the map. Theidentities of the buried objects are given in Table 2.

This site presented a surprising number of challenges tomine detection and data from it are valuable in that theyillustrate problems that could be encountered in realdemining operations. The target set was deliberately selectedto be stressing to our sensors. In contrast to real mines,essentially all of which contain some metal, roughly half themine surrogates were metal-free. In addition, some of thesurrogate mines are quite small (only 1.5 inches in diameter)and undetectable to all of the sensors. These objects wereredesignated as clutter. The site has been intermittently used

for various engineering experiments for more than 40 years,which produced a significant amount of small metallic debris.Consistent with our goal of achieving realistic environmentalconditions, the test area was not cleared prior to emplacingthe targets. As a result, during two years of testing, roughly100 metallic fragments and a number of stones were located in(and, subsequently, removed from) the region. When thetargets were initially emplaced, a lush grass cover waspresent in the area, which was subsequently removed toimprove the performance of the IR camera. The soil contains alarge amount of clay, which has a negative effect on GPRperformance. The surface of the mine field contains a numberof topological irregularities but it is planar to within anestimated variation of�2 inches. The objects in this field hadbeen in situ for more that 18 months at the time these datawere acquired.

Data were acquired along the paths shown in Fig. 6. Thesmall circles are the target grid points shown previously. TheGPR samples were acquired at � 0.5 inch intervals alongnorth-south (N-S) lines spaced every two inches east-west(E-W). The EMI sensor acquired samples at � 1 inchintervals along N-S lines spaced six inches E-W. TheIR camera was positioned on the roof of a two-story buildingadjacent to the test site. The camera's field of view did notpermit us to sample the entire mine field with an acceptablepixel density and a sequence of eight images was necessaryas indicated by the trapezoids. Styrofoam fiducial markers


Fig. 5. Plan view of the surrogate mine and clutter test grid. The surface of the mine grid is bare soil. The surrounding area is covered with grass.

were placed on the region to permit later image warping andregistration, which are indicated by squares in Fig. 6.

4.3 Performance of Individual Sensors

For each sensor i, feature vectors �i were extracted usingthe signal processing algorithms discussed above andsupplied to sensor-specific classifiers Pr�uij�i; ti�. Resultsfor the binary detection problem involving hypothesesH1 � }nonmine} and H2 � }mine} are reported here. Theprior probabilities for this site are Pr�H0� � 28=40 andPr�H1� � 12=40. It is important to note that the number ofmine surrogates being sampled is small. The resultsobtained must be interpretted in light of this fact and,hence, it is difficult to draw general conclusions.

To compute PD and PF , the test area was divided into a

large number of square cells (280). A cell was considered tocontain a detection if at least four adjacent detections werepresent. We computed the false alarm probability as the

number of false detections divided by the total number ofcells not occupied by mines.

To permit comparison between sensors, we have takenall intermediate sensor-specific hypotheses hki to be Hk,

even though some surrogates are undetectable to somesensors. It is known that with sufficient training data

backpropagation neural networks will approximate an a

posteriori density [21], and the outputs of such a network

(normalized to a unit sum) were used to approximate the

required a posteriori probabilities. The number of input and

output nodes for these networks were defined by the sizes

of �i and K, respectively. The number of hidden nodes

were 3, 7, and 6 for the GPR, EMI, and IR sensors,

respectively. Target detections ui were produced by thresh-

olding the network outputs at level ti. Leave-one-out

training and validation was used in all of the results.

Because networks trained with random weight initializa-

tions may converge to spurious local error minima, several

trials were conducted and the best results were retained.Figs. 7, 8, and 9 present binary detection maps for each

sensor, which were generated by choosing appropriate

detection thresholds ti and discarding regions with small

number of adjacent detections. The dark masses on these

maps indicate detections, while circles represent the

locations of the declared mine surrogates. Detection cells


TABLE 2Description of the Objects Buried in the Mine Test Grid

For the planar objects indicated by an asterisk, dimensions are length and width.

Fig. 6. Locations of sample points for the sensor suite.

Fig. 7. Detection map obtained using EMI sensor.

Fig. 8. Detection map obtained using IR sensor.

for the targets are indicated by squares. It is clear from these

results that the EMI and IR sensors have a high false alarm

rate when all targets are detected. The poor performance of

the EMI sensor was anticipated because most of the mine

surrogates in our test grid are nonmetallic and the site

contains a large quantity of metallic clutter. The poor

performance of the IR sensor was not anticipated, but may

be due to the relatively large number of surface irregula-

rities. For the threshold chosen here, the GPR sensor shows

reasonably good performance, with only a single missed

detection and a moderate false alarm rate. Detection of the

missed mine, however, is problematic. The performance of

these sensors can be compared quantitatively using receiver

operating characteristic (ROC) curves, as shown in Fig. 10.

These results confirm the findings shown in the detection

maps. In particular, the inability of the GPR to detect all

mines at a reasonable false alarm rate is clear.

4.4 Performance of Fusion Algorithms

For decision-level fusion, we used the ªgood thresholdº

approximation described in Section 3.2 to avoid the search

over all possible sensor thresholds ti implied in (25). The

EMI and IR sensor thresholds were selected such that all

expected targets (i.e., targets with metal for the EMI sensor

and targets that present a sizable thermal discontinuity for

the IR sensor) were detected while minimizing clutter

detections. The criterion used for selecting the GPR thresh-

old was the ªkneeº in the ROC curve in Fig. 10. The

resulting individual sensor PMiand PFi

values are shown in

Table 3. The detections ui for these thresholds comprise the

inputs ui for the decision-level fusion algorithms and are

shown in the foregoing individual sensor detection maps.

The local confidences Pr�uij�i; ti� required for the soft-

decision fusion scheme of (27) were set to the a posteriori

probability estimates produced by the corresponding

classifier output. The ROC curve for decision-level fusion

appears in Fig. 11.

Comparing Figs. 10 and 11, we see that hard-decision

fusion based on (25) offers little benefit over the GPR sensor

alone. Based on the form of (25), which most strongly weights

the most reliable sensors, this result was expected. The

performance of soft-decision fusion, however, is somewhat

better. It is clear that with soft-decision fusion, PD � 1 can be

achieved with a smaller PF , which is a significant

improvement over the best individual sensor performance.

The detection map obtained for soft-decision fusion is shown

in Fig. 12. The detection map for hard-fusion is not shown,

because it is nearly identical to the GPR detection map.


Fig. 9. Detection map obtained using the GPR sensor.

TABLE 3Individual Sensor PF and PM Using ªGoodº Thresholds

Fig. 10. Receiver operating characteristic (ROC) curves of individual

sensors.

Fig. 11. Receiver operating characteristic (ROC) curves for three types

of fusion.

Fig. 12. Detection map obtained using soft-decision fusion.

For feature-level fusion, the sensor feature vectors �i wereconcatentated and used in a single classifier (cf. (8)), resultingin the ROC curve shown in Fig. 11. As done for the individualsensors, the classifier Pr�Hkj�̂� was approximated by abackpropagation neural network. A total of 14 hidden nodes

were used in this network.Using as a figure of merit, the smallest PF at which

PD � 1, we see that the feature-fused system is significantlybetter than the individual sensors and marginally betterthan the soft-decision fusion case. The detection mapproduced by the feature-fused system, corresponding tothe largest threshold that can achieve PD � 1, is given in

Fig. 13. Comparing the soft-decision case in Fig. 12 and thefeature-level case in Fig. 13, the reduction in false alarmrate indicated by the ROC curve (roughly 40 percent) isevident.

5 SUMMARY AND CONCLUSIONS

We have developed a feature-level fusion technique fornoncommensurate sensor data sampled at noncoincidentlocations. The features used for fusion were extracted fromspatial signatures of targets by applying nonlinear optimi-zation techniques to data collected in a neighborhood of thelocation of interest. The maximum a posteriori approxima-tion was used to simplify the exact fusion formulation to aform that was practical to implement. For the special case ofnormal clutter and normal linear features, fusion can beexpressed as the Bayesian linear model for which a compactclosed form expression exists. This result was used todemonstrate the importance of accurate sensor positioninformation. We also discussed several decision-level fusionschemes that can be used for these data.

We tested the fusion algorithms on noncommensuratenoncoincidently sampled data acquired by EMI, GPR, andIR sensors over a test field containing mine surrogates andboth deliberate and unknown clutter. The targets and theclutter present in the test site were both very challenging.Although the number of mine surrogates sampled wassmall, the results presented here indicate that the perfor-mance of feature-level fusion and soft-decision fusion canbe significantly better than that of the individual sensors.This performance enhancement is encouraging, especiallywhen we recognize that the IR and EMI sensors were onlymarginally effective due to both the heavy clutter at the testsite and our selection of surrogate targets. As expected,hard-decision fusion showed little improvement over theperformance of the best individual sensor since thealgorithm most strongly weights the most efffective sensors.

Overall, we have shown that feature-level and soft-

decision level fusion of noncoincidently sampled EMI, IR,

and GPR data can result in significant improvements in

mine detection performance. We found a small additional

benefit in using feature-level fusion, which provided a

40 percent reduction in the false alarm rate beyond the soft-

decision fusion case. The feature-level fusion algorithm also

provides an explicit method for dealing with position

errors, which is not available through the decision-level

fusion algorithms. The computational costs of decision-level

and feature-level fusion algorithms are approximately equal

since the computational expense involved in fusion is

dominated by features estimation, and all methods of

detection must perform this processing. There is, however,

a small penalty for feature-level fusion since the classifier

must be somewhat more complex to account for the greater

number of inputs.These results are encouraging but the small sample size

of our data set suggests that a larger study be done to

confirm these results. A data collection has been done at a

larger minefield operated by the US Army at Fort A.P. Hill,

Virginia. That study is now complete, and the results will be

reported in the future.

ACKNOWLEDGMENTS

This project was supported by funds from Duke Universityunder an award from the ARO (the OSD MURI program).The findings, opinions, and recommendations expressedtherein are those of the authors and are not necessarilythose of Duke University or the ARO. A preliminaryversion of this paper was presented at the 1999 SPIEAeroSense Conference, Orlando, Florida.

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Fig. 13. Detection map obtained using feature-level fusion.

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[19] S. Nag, L. Peters Jr., I.J. Gupta, and C.C. Chen, ªRamp Responsefor the Detection of Anti-Personel Mines,º Proc. SPIE: Detectionand Remediation Technologies for Mines and Minelike Targets IV,A.C. Dubey, J.F. Harvey, J.T. Broach, and R.E. Dugan, eds.,vol. 3710, pp. 1313-1322, 1999.

[20] I.K. Sendur and B.A. Baertlein, ªTechniques for Improving BuriedMine Detection in Thermal IR Imagery,º Proc. SPIE: Detection andRemediation Technologies for Mines and Minelike Targets IV,A.C. Dubey, J.F. Harvey, J.T. Broach, and R.E. Dugan, eds.,vol. 3710, pp. 1272-1283, 1999.

[21] M.D. Richard and R.P. Lippmann, ªNeural Network ClassifiersEstimate Bayesian a Posteriori Probabilities,º Neural Computation,vol. 3, pp. 461-483, 1991.

Ajith H. Gunatilaka received the BSc degree inelectronic and telecommunication engineeringfrom the University of Moratuwa, Sri Lanka, in1990. In 1994, he obtained the MS degree inoptical sciences and engineering from theUniversity of Central Florida. He received thePhD degree in electrical engineering from theOhio State University in March 1990. He was agraduate research associate at the Electro-Science Laboratory of The Ohio State University

from 1994 to 2000. He is currently a member of technical staff at LucentTechnologies in Columbus, Ohio. He is a member of the IEEE.

Brian A. Baertlein received the PhD in electricalengineering from the University of Arizona in1988. His professional career has includedanalyses of sensor systems of various types,development of detection and estimation algo-rithms, and work in sensor fusion, scattering andpropagation phenomena, antennas, and electro-magnetic compatibility. He is currently a re-search scientist and adjunct associate professor

of electrical engineering at The Ohio State University (OSU) Electro-Science Laboratory (ESL). Before joining OSU, he was a senior scientistwith several small businesses doing work for the US Department ofDefense and the Department of Energy. He is am member of the IEEE.

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